...in the condo parking lot (private property) last night and woke up this morning to see the car had been towed.

The grandma's vehicle was unregistered.

I know in Provo, the tow truck company has to have proof of the property owner requesting a tow. My guess is the condo owner in this situation did not request a tow. But who knows. I guess it doesn't matter if Orem doesn't have laws like Provo's.

Also, is an unregistered vehicle not allowed to be parked in a condo parking lot of an owner of one of the condos?

Kinda an odd situation for several reasons.